/*
 * @lc app=leetcode.cn id=74 lang=cpp
 *
 * [74] 搜索二维矩阵
 *
 * https://leetcode-cn.com/problems/search-a-2d-matrix/description/
 *
 * algorithms
 * Medium (37.68%)
 * Likes:    153
 * Dislikes: 0
 * Total Accepted:    37.1K
 * Total Submissions: 98.6K
 * Testcase Example:  '[[1,3,5,7],[10,11,16,20],[23,30,34,50]]\n3'
 *
 * 编写一个高效的算法来判断 m x n 矩阵中，是否存在一个目标值。该矩阵具有如下特性：
 * 
 * 
 * 每行中的整数从左到右按升序排列。
 * 每行的第一个整数大于前一行的最后一个整数。
 * 
 * 
 * 示例 1:
 * 
 * 输入:
 * matrix = [
 * ⁠ [1,   3,  5,  7],
 * ⁠ [10, 11, 16, 20],
 * ⁠ [23, 30, 34, 50]
 * ]
 * target = 3
 * 输出: true
 * 
 * 
 * 示例 2:
 * 
 * 输入:
 * matrix = [
 * ⁠ [1,   3,  5,  7],
 * ⁠ [10, 11, 16, 20],
 * ⁠ [23, 30, 34, 50]
 * ]
 * target = 13
 * 输出: false
 * 
 */

#include <vector>

using namespace std;

// @lc code=start
class Solution
{
public:
    bool searchMatrix(vector<vector<int>> &matrix, int target)
    {
        int m = matrix.size();
        if (m == 0)
            return false;
        int n = matrix[0].size();

        int left = 0;
        int right = m * n - 1;
        while (left <= right)
        {
            int mid = (left + right) >> 1;
            int pivot_element = matrix[mid / n][mid % n];
            if (pivot_element == target)
                return true;
            else if (pivot_element > target)
                right = mid - 1;
            else
                left = mid + 1;
        }
        return false;
    }
};
// @lc code=end
